Mathematics 9709 · AS & A Level · Circular measure

Circular measure — practice question

The diagram illustrates a metal plate $ABCDEF$ formed by removing the two shaded regions from a circle of radius $10$ cm and centre $O$. The parallel sides $AB$ and $ED$ each have length $12$ cm.
(i)[2]

Show that angle $DOE$ has a value of $1.287$ radians, correct to $4$ significant figures.

(ii)[3]

Find the total perimeter of the metal plate.

(iii)[3]

Find the total area of the metal plate.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Applies $\sin(\tfrac12\theta)=\tfrac{6}{10}$.

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